The fixed point action for the Schwinger model: a perturbative approach

We compute the fixed point action of a properly defined renormalization group transformation for the Schwinger model through an expansion in the gauge field. It is local, with couplings exponentially suppressed with the distance. We check its perfection by computing the 1-loop mass gap at finite spatial volume, finding only exponentially vanishing cut off effects, in contrast with the standard action, which is affected by large power-like cut off effects. We point out that the 1-loop mass gap calculation provides a check of the classical perfection of the fixed point action, and not of the 1-loop perfection, as could be naively expected.Comment: 34 pages, LaTeX, 8 figures, uses style [epsfig

Lattice supersymmetric Ward identities

SUSY Ward identities for the N=1 SU(2) SUSY Yang-Mills theory are studied on the lattice in a non-perturbative numerical approach. As a result a determination of the subtracted gluino mass is obtained.Comment: 3 pages, 2 figures, Lattice2001(higgssusy

On the 1-loop lattice perturbation theory of the supersymmetric Ward identities

The one loop corrections to the supersymmetric Ward identities (WIs) in the discretized N=1 SU(2) supersymmetric Yang-Mills theory can be investigated by means of lattice perturbation theory. The supersymmetry (SUSY) is explicitly broken by the lattice discretization as well as by the introduction of Wilson fermions. However, the renormalization of the supercurrent can be carried out in a scheme that restores the nominal continuum WIs. We present our work in progress which is concerned with the 1-loop renormalization of the local supercurrent, i.e. with the perturbative computation of the corresponding renormalization constants and mixing coefficients.Comment: Lattice 2000 (Supersymmetry), 4 pges, 2 figure

SUSY Ward identities in N=1 SYM theory on the lattice

The SUSY Ward identities (WIs) for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos) are considered. The study is performed in the framework of a Monte Carlo simulation of the model with light dynamical gluinos. The renormalization and mixing constants of the lattice SUSY current $Z_S$ and $Z_T$ and the additively renormalized gluino mass $m_S$ are unknown parameters of the SUSY WIs. Using suitable on-shell combinations of the WIs, the ratios $Z_T/Z_S$ and $m_S/Z_S$ are determined non-perturbatively at one value of the coupling constant $g_0$ and two values of the hopping parameter $\kappa$.Comment: Lattice 2000 (Supersymmetry), 4 pages, 2 figure

The absence of cut--off effects for the fixed point action in 1--loop perturbation theory

In order to support the formal renormalization group arguments that the fixed point action of an asymptotically free model gives cut--off independent physical predictions in 1--loop perturbation theory, we calculate the finite volume mass--gap $m(L)$ in the non--linear $\sigma$--model. No cut--off effect of the type $g^4\left(a/L\right)^n$ is seen for any $n$. The results are compared with those of the standard and tree level improved Symanzik actions.Comment: 8 pages (latex) + 1 figure (Postscript), uuencode

Kaon and D meson masses with Nf = 2+1+1 twisted mass lattice QCD

We discuss the computation of the kaon and D meson masses in the Nf = 2+1+1 twisted mass lattice QCD setup, where explicit heavy flavor and parity breaking occurs at finite lattice spacing. We present three methods suitable in this context and verify their consistency

SUSY Ward identities in 1-loop perturbation theory

We present preliminary results of a study of the supersymmetric (SUSY) Ward identities (WIs) for the N=1 SU(2) SUSY Yang-Mills theory in the context of one-loop lattice perturbation theory. The supersymmetry on the lattice is explicitly broken by the gluino mass and the lattice artifacts. However, the renormalization of the supercurrent can be carried out in a scheme that restores the nominal continuum WIs. The perturbative calculation of the renormalization constants and mixing coefficients for the local supercurrent is presented.Comment: Lattice2001(higgssusy); 3 page

Scaling and topology in the 2-d O(3) σ\sigma-model on the lattice with the fixed point action

We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap confirms the good properties of scaling of the fixed point action. Concerning the topology, lattice classical solutions are proved to be very stable under local minimization of the action; this outcome ensures the reliability of the cooling method for the computation of the topological susceptibility, which indeed reproduces the results of the field theoretical approach. Disagreement is instead observed with a different approach in which the fixed point topological charge operator is used: we argue that the discrepancy is related to the ultraviolet dominated nature of the model.Comment: 24 pages (Latex) + 8 figures (PostScript) in a uuencoded compressed tar fil

Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index Theorem. We show by explicit computation that it is possible to find an accurate approximation to the Fixed Point Dirac operator containing only very local couplings.Comment: 38 pages, LaTeX, 3 figures, uses style [epsfig], a few comments and relevant references adde